Small Question on What Points the Equation has Solutions for y in terms of x,z.

[mmmboh]

Hi this is the question, I already finished it basically, there is just one small thing I am unsure about

So I let that equation be F, and I found F^y, it is Ze^yz-x²z/y...so I know this equation can't equal zero if I want there to be a solution for y in terms of x and z, my question is what I do about the x²z/y term...is y allowed to equal 0? If that is the case then the equation can equal negative infinity, I'm not sure if this is legal or not, when I think about a system of equations and it's relation to the determinant, it doesn't really make sense for it to be equal to infinity...but if this is legal, I'm assuming x²z/y can't equal 0/0 because then it is in indeterminate form...

So can y=0?

Thanks :)

 

[lippyka]

No, y cannot equal 0. If y is equal to 0 then the equation would be undefined, since you can't divide by 0. Therefore, x2z/y cannot equal 0/0 and the equation cannot equal negative infinity.